{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:22A3PQQXFZRQTJRUVGSZNML55C","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6a6f4b21d660ea11ce906573b049bbf48eb0091601a04a4d25327b5c7989e747","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-17T20:49:39Z","title_canon_sha256":"3b04a6a38f13ebe68b8fdcdcfba0e4901a13ecb2a051728c829973ad970186f3"},"schema_version":"1.0","source":{"id":"1011.4056","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.4056","created_at":"2026-05-18T03:56:22Z"},{"alias_kind":"arxiv_version","alias_value":"1011.4056v2","created_at":"2026-05-18T03:56:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.4056","created_at":"2026-05-18T03:56:22Z"},{"alias_kind":"pith_short_12","alias_value":"22A3PQQXFZRQ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"22A3PQQXFZRQTJRU","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"22A3PQQX","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:42a20b4ff7faebcdbe37e844712d6bd78beec5663fabaf5e83d0884c5c1bac5f","target":"graph","created_at":"2026-05-18T03:56:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let T be a rooted supercritical multi-type Galton-Watson (MGW) tree with types coming from a finite alphabet, conditioned to non-extinction. The lambda-biased random walk (X_t, t>=0) on T is the nearest-neighbor random walk which, when at a vertex v with d(v) offspring, moves closer to the root with probability lambda/[lambda+d(v)], and to each of the offspring with probability 1/[lambda+d(v)]. This walk is recurrent for lambda>=rho and transient for 0<lambda<rho, with rho the Perron-Frobenius eigenvalue for the (assumed) irreducible matrix of expected offspring numbers. Subject to finite mome","authors_text":"Amir Dembo, Nike Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-17T20:49:39Z","title":"Central limit theorem for biased random walk on multi-type Galton-Watson trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4056","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:35940fe8c1e1923e6c6b88ec996621fb13e0955052a157e8c5344c941e0a794f","target":"record","created_at":"2026-05-18T03:56:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6a6f4b21d660ea11ce906573b049bbf48eb0091601a04a4d25327b5c7989e747","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-17T20:49:39Z","title_canon_sha256":"3b04a6a38f13ebe68b8fdcdcfba0e4901a13ecb2a051728c829973ad970186f3"},"schema_version":"1.0","source":{"id":"1011.4056","kind":"arxiv","version":2}},"canonical_sha256":"d681b7c2172e6309a634a9a596b17de8833eb0eae7fc56ed90d1f7f15fdcc7e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d681b7c2172e6309a634a9a596b17de8833eb0eae7fc56ed90d1f7f15fdcc7e6","first_computed_at":"2026-05-18T03:56:22.789059Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:22.789059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pEzkO5SsC8RkfIxEyjlgUXB9s3QUF+FGtG2+HPCIBj5xMrYHz0pUa4r+hBYJtbFlvMHi7YIuka1jY4f4cT4HCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:22.789775Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.4056","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35940fe8c1e1923e6c6b88ec996621fb13e0955052a157e8c5344c941e0a794f","sha256:42a20b4ff7faebcdbe37e844712d6bd78beec5663fabaf5e83d0884c5c1bac5f"],"state_sha256":"1d4ba39ce32471a46103c7186294e690c7a1fa67340228c62512068d75482af6"}